Pulse Documentation

name: op-test-kendall-tau
description: Concordance-based correlation between Field and Field2; buffered O(n²) pair count under tie correction.
kind: operator
category: TEST
operator: TEST_KENDALL_TAU
type: reference
applies_to: process, compose, predict
examples_tags: [hypothesis-test, tier-1-test, nonparametric, correlation-analysis, small-sample, buffered-pipeline]

Tests emit statistic / p-value / effect size; no Response.Components.

Use when

Measures how often pairs of rows agree in order on two numeric fields: a rank-based link suited to small samples and ties.

Questions it answers:

• In a small panel, do judges who score one entry higher also score the other higher?
• Do two coarse rating scales tend to agree?

Use something else:

• TEST_SPEARMAN_R when the data are large; its cost grows with the square of the row count.

Params

• alpha — float, default 0.05, in (0, 1).
• weight — slot weight (null opts out), kind frequency only (a probability weight is PULSE_WEIGHT_UNSUPPORTED naming the kind): a row pair counts w_i·w_j times — equals τ-b on the expanded pairs. Details add sum_weights beside n (raw rows); pair counts become Σ w_i·w_j.

Slot params: Field (required, numeric), Field2 (required, numeric).

• multiplicity — optional {method, family}; adds p_adjusted beside the raw p (multiplicity-correction).

Inputs

Field — numeric: u4/u8/u16/u32/u64, f32/f64, date. Field2 — numeric (same set).

Output

Statistic = τ_b (Kendall tau-b, [-1, 1]); PValue two-sided via normal approximation with tie-variance adjustment. Details.concordant, Details.discordant, Details.ties_x, Details.ties_y, Details.s, Details.var_s, Details.z, Details.n.

Reading the output

• statistic: Kendall’s tau-b, from -1 to +1: the share of row pairs that are ordered the same way on both fields minus the share ordered the opposite way, adjusted for ties.
  • Sign: positive means the two fields tend to rise together; negative means one field tends to fall as the other rises.
  • Caveat: Correlation is not causation: a third factor may drive both fields.
• p_value: a p-value. Below alpha (0.05 unless the request sets another) the result is called significant; that is not the same as important, so read the effect size for how big it is.

Gotchas

• Buffered O(n²) pair enumeration — expensive on large n; filter or pre-sample first.
• Suits small samples and heavy ties (tau-b corrects for ties in either column).
• Distribution-free; no normality assumption.
• Tier-2 variant TEST_KENDALL_TAU/tau_b_post runs over result columns.
• For high-cardinality numeric fields the O(n²) cost dominates.

See

• pulse_examples_search tags=[correlation-analysis]
• Skills: statistical-testing, op-test-spearman-r, op-test-pearson-r